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When this standard says “generate two numerical patterns using two given rules” how should the word given be interpreted? Should this be interpreted literally that students should always be given the rules in order to generate the patterns or does the phrase given rules simply imply that any pattern will have a given rule that it follows?
The first interpretation is the correct one: the rules for the patterns are given to the student. But then students might see a relationship between the two patterns that is not given explicitly, but that follows from the two rules.
Can students in Gr. 5 be expected to generate/continue patterns given the first few items in a pattern (in lieu of being given a rule in words)? Also, could two sets of data be given in a table format and students be expected to use the established patterns and the relationship between the two sets of data to find a missing value in one pattern that corresponds to a given value in another pattern?
The problem is that any finite sequence can be continued in a variety of ways and by itself doesn’t determine a unique pattern. There are illustrations of this in the short section on “the problem with patterns” in the Functions Progression. It can be downloaded here: http://ime.math.arizona.edu/progressions/
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